Temporal Vector Visibility Graph: A Tool for Complexity Analysis of Multivariate Time Series

Abstract

The family of visibility algorithms provides a new point of view to describe time series by transforming them into networks. In this paper, we propound a new visibility algorithm named Temporal Vector Visibility graph [Formula: see text], which maps the multivariate time series to a directed network. Computed by the [Formula: see text] and [Formula: see text] degree distributions obtained from the [Formula: see text], these statistics such as the Kullback–Leibler divergence (KLD), the normalized Shannon entropy and the statistical complexity measure, are introduced to assess the complexity of time series. Furthermore, we also apply the Multivariate Multiscale Entropy Plane (MMEP) to evaluate the complexity of multivariate time series. The experimental results of eight different types of time series verify the effectiveness of our method. Subsequently, this method is employed to explore the complexity characteristics of financial time series and classify different stock markets. Our research reveals that this method is capable of investigating the physical structures of financial time series.